OFFSET
0,3
FORMULA
a(n) = A368548(2^n-1).
If n is odd, a(n) = binomial(2*(2^((n-1)/2)-1),2^((n-1)/2)-1) + 2*Sum_{i=0..(n-3)/2)} binomial(2^i+2^(n-i-1)-2,2^i-1).
If n is even, a(n) = 2*Sum_{i=0..n/2-1} binomial(2^i+2^(n-i-1)-2,2^i-1).
log(a(n)) ~ c * 2^(n/2), where c = 3*log(3)/2 - log(2) if n is even and c = sqrt(2)*log(2) if n is odd. - Vaclav Kotesovec, Feb 10 2024
MATHEMATICA
Table[Sum[Binomial[2^i+2^(n-i-1)-2, 2^i-1], {i, 0, n-1}], {n, 0, 14}] (* James C. McMahon, Feb 08 2024 *)
PROG
(Python)
from math import comb
def A370070(n): return (sum(comb((1<<i)+(1<<n-i-1)-2, (1<<i)-1) for i in range(n>>1))<<1) + (comb(((1<<(n>>1))-1)<<1, (1<<(n>>1))-1) if n&1 else 0)
CROSSREFS
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Feb 08 2024
STATUS
approved